Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms

Márcio R.A. Gouveia, Jaume Llibre, Douglas D. Novaes, Claudio Pessoa

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

© 2015 Elsevier Inc. We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane σ which admits an invariant hyperplane Ω transversal to σ containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n=3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
Original languageEnglish
Pages (from-to)6108-6129
JournalJournal of Differential Equations
Volume260
Issue number7
DOIs
Publication statusPublished - 5 Apr 2016

Keywords

  • Crossing periodic solutions
  • Limit cycles
  • Lyapunov-Schmidt reduction
  • Normal forms
  • Piecewise differential system

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